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- W4296581269 abstract "The paper deals with partitions of hypergraphs into induced subhypergraphs satisfying constraints on their degeneracy. Our hypergraphs may have multiple edges, but no loops. Given a hypergraph $H$ and a sequence $f=(f_1,f_2, ldots, f_p)$ of $pgeq 1$ vertex functions $f_i:V(H) to mathbb{N}_0$ such that $f_1(v)+f_2(v)+ cdots + f_p(v)geq d_H(v)$ for all $vin V(H)$, we want to find a sequence $(H_1,H_2, ldots, H_p)$ of vertex disjoint induced subhypergraphs containing all vertices of $H$ such that each hypergraph $H_i$ is strictly $f_i$-degenerate, that is, for every non-empty subhypergraph $H'subseteq H_i$ there is a vertex $vin V(H')$ such that $d_{H'}(v)<f_i(v)$. Our main result in this paper says that such a sequence of hypergraphs exists if and only if $(H,f)$ is not a so-called hard pair. Hard pairs form a recursively defined family of configurations, obtained from three basic types of configurations by the operation of merging a vertex. Our main result has several interesting applications related to generalized hypergraph coloring problems." @default.
- W4296581269 created "2022-09-22" @default.
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- W4296581269 date "2018-04-13" @default.
- W4296581269 modified "2023-09-29" @default.
- W4296581269 title "Partitions of hypergraphs under variable degeneracy constraints" @default.
- W4296581269 doi "https://doi.org/10.48550/arxiv.1804.04894" @default.
- W4296581269 hasPublicationYear "2018" @default.
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